Domanda del libro di testo
Find the coordinates of the vertex for the parabola defined by the given quadratic function. f(x)=−2(x+1)2+5
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Ch. 3 - Polynomial and Rational Functions
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 4, Problema 11
Write an equation that expresses each relationship. Then solve the equation for y. x varies jointly as y and z.
Guida verificata passo dopo passo1
Understand the phrase "x varies jointly as y and z" means that x is directly proportional to the product of y and z. This can be expressed as an equation involving a constant of proportionality, say k.
Write the joint variation equation as \(x = k \cdot y \cdot z\), where \(k\) is a constant.
To solve the equation for \(y\), isolate \(y\) on one side. Start by dividing both sides of the equation by \(kz\) (assuming \(k \neq 0\) and \(z \neq 0\)):
\[ y = \frac{x}{kz} \]
This equation expresses \(y\) in terms of \(x\), \(k\), and \(z\). If you have specific values for \(x\), \(k\), and \(z\), you can substitute them to find \(y\).
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Joint Variation
Joint variation describes a relationship where one variable varies directly as the product of two or more other variables. In this case, x varies jointly as y and z means x = kyz, where k is the constant of proportionality.
Formulating Equations from Word Problems
Translating a verbal relationship into an algebraic equation involves identifying variables and their relationships. Here, recognizing 'x varies jointly as y and z' helps write the equation x = kyz, setting the foundation for solving for a specific variable.
Video consigliato:
05:56
Introduction to Rational Equations
Solving for a Variable
Solving for y means isolating y on one side of the equation. Starting from x = kyz, divide both sides by kz (assuming k and z are nonzero) to get y = x / (kz), which expresses y explicitly in terms of x, k, and z.
Video consigliato:
05:28Equations with Two Variables
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In Exercises 9–16, a) List all possible rational zeros. b) Use synthetic division to test the possible rational zeros and find an actual zero. c) Use the quotient from part (b) to find the remaining zeros of the polynomial function. f(x)=2x3−3x2−11x+6
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